Table of contents¶

Context

Download the latest data

The purposes of this project

Main Findings

Importing packages and reading file

Data wrangling

Exploratory data analysis

Model estimation and prediction

  • Data Preparation for modeling
  • Estimation
  • Prediction
  • Hyperparameter tuning

Model selection and final results

Context ¶

How is Airbnb really being used in and affecting the neighbourhoods of your city? Airbnb claims to be part of the 'sharing economy' and disrupting the hotel industry. However, data shows that the majority of Airbnb listings in most cities are entire homes, many of which are rented all year round - disrupting housing and communities.

(source: https://insideairbnb.com/)

Download the latest data ¶

https://insideairbnb.com/get-the-data/ image.png

The purposes of this project: ¶

  • To gain insights into listings and identify the optimal model for price prediction.

Main Findings: ¶

  • Airbnb in London consists of around 55,035 hosts and 90,848 listings.
  • The top ten hosts individually have more than 150 listings.
  • The most popular area is Westminster, accounting for more than 11% of the listings.
  • At least 95% of the market is occupied by rooms with prices lower than 500 pounds per night.
  • The pricing settings are similar between Entire home/apt and Hotel room, as well as between Private room and Shared room.
  • In Entire home/apt, only 5% of the listings require a minimum stay of more than 20 nights.
  • The services offered are primarily designed for short-term rental arrangements.
  • Over the past 12 months, the average minimum income was about 3172 pounds.
  • The best model for price prediction is the Random Forest, and the model explains about 63% of the variation in price.

Import packages and read file ¶

In [1]:
# Import necessary packages
import time
import warnings
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import plotly
import plotly.express as px
import scipy.stats as stats
import seaborn as sns
import statsmodels.api as sm

from sklearn.model_selection import train_test_split, GridSearchCV
from sklearn.preprocessing import RobustScaler
from sklearn import metrics
from sklearn.linear_model import LinearRegression, ElasticNet
from sklearn.neighbors import KNeighborsRegressor
from sklearn.tree import DecisionTreeRegressor
from sklearn.ensemble import RandomForestRegressor
from sklearn.neural_network import MLPRegressor
from xgboost import XGBRegressor

warnings.filterwarnings("ignore")
plotly.offline.init_notebook_mode()
In [2]:
# Read the csv file downloaded from the website
raw_data = pd.read_csv("listings.csv")
In [3]:
# Summary of the raw data
raw_data.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 90852 entries, 0 to 90851
Data columns (total 75 columns):
 #   Column                                        Non-Null Count  Dtype  
---  ------                                        --------------  -----  
 0   id                                            90852 non-null  int64  
 1   listing_url                                   90852 non-null  object 
 2   scrape_id                                     90852 non-null  int64  
 3   last_scraped                                  90852 non-null  object 
 4   source                                        90852 non-null  object 
 5   name                                          90852 non-null  object 
 6   description                                   87851 non-null  object 
 7   neighborhood_overview                         47521 non-null  object 
 8   picture_url                                   90842 non-null  object 
 9   host_id                                       90852 non-null  int64  
 10  host_url                                      90852 non-null  object 
 11  host_name                                     90847 non-null  object 
 12  host_since                                    90847 non-null  object 
 13  host_location                                 70566 non-null  object 
 14  host_about                                    46814 non-null  object 
 15  host_response_time                            57797 non-null  object 
 16  host_response_rate                            57797 non-null  object 
 17  host_acceptance_rate                          65213 non-null  object 
 18  host_is_superhost                             90463 non-null  object 
 19  host_thumbnail_url                            90847 non-null  object 
 20  host_picture_url                              90847 non-null  object 
 21  host_neighbourhood                            46955 non-null  object 
 22  host_listings_count                           90847 non-null  float64
 23  host_total_listings_count                     90847 non-null  float64
 24  host_verifications                            90847 non-null  object 
 25  host_has_profile_pic                          90847 non-null  object 
 26  host_identity_verified                        90847 non-null  object 
 27  neighbourhood                                 47522 non-null  object 
 28  neighbourhood_cleansed                        90852 non-null  object 
 29  neighbourhood_group_cleansed                  0 non-null      float64
 30  latitude                                      90852 non-null  float64
 31  longitude                                     90852 non-null  float64
 32  property_type                                 90852 non-null  object 
 33  room_type                                     90852 non-null  object 
 34  accommodates                                  90852 non-null  int64  
 35  bathrooms                                     57894 non-null  float64
 36  bathrooms_text                                90722 non-null  object 
 37  bedrooms                                      78118 non-null  float64
 38  beds                                          57837 non-null  float64
 39  amenities                                     90852 non-null  object 
 40  price                                         57885 non-null  object 
 41  minimum_nights                                90852 non-null  int64  
 42  maximum_nights                                90852 non-null  int64  
 43  minimum_minimum_nights                        90851 non-null  float64
 44  maximum_minimum_nights                        90851 non-null  float64
 45  minimum_maximum_nights                        90851 non-null  float64
 46  maximum_maximum_nights                        90851 non-null  float64
 47  minimum_nights_avg_ntm                        90851 non-null  float64
 48  maximum_nights_avg_ntm                        90851 non-null  float64
 49  calendar_updated                              0 non-null      float64
 50  has_availability                              86773 non-null  object 
 51  availability_30                               90852 non-null  int64  
 52  availability_60                               90852 non-null  int64  
 53  availability_90                               90852 non-null  int64  
 54  availability_365                              90852 non-null  int64  
 55  calendar_last_scraped                         90852 non-null  object 
 56  number_of_reviews                             90852 non-null  int64  
 57  number_of_reviews_ltm                         90852 non-null  int64  
 58  number_of_reviews_l30d                        90852 non-null  int64  
 59  first_review                                  65869 non-null  object 
 60  last_review                                   65869 non-null  object 
 61  review_scores_rating                          65869 non-null  float64
 62  review_scores_accuracy                        65838 non-null  float64
 63  review_scores_cleanliness                     65843 non-null  float64
 64  review_scores_checkin                         65808 non-null  float64
 65  review_scores_communication                   65833 non-null  float64
 66  review_scores_location                        65808 non-null  float64
 67  review_scores_value                           65806 non-null  float64
 68  license                                       0 non-null      float64
 69  instant_bookable                              90852 non-null  object 
 70  calculated_host_listings_count                90852 non-null  int64  
 71  calculated_host_listings_count_entire_homes   90852 non-null  int64  
 72  calculated_host_listings_count_private_rooms  90852 non-null  int64  
 73  calculated_host_listings_count_shared_rooms   90852 non-null  int64  
 74  reviews_per_month                             65869 non-null  float64
dtypes: float64(24), int64(17), object(34)
memory usage: 52.0+ MB

Data wrangling ¶

Select variables which are similar to the kaggle dataset

https://www.kaggle.com/datasets/dgomonov/new-york-city-airbnb-open-data/data

  • id: Airbnb's unique identifier for the listing.
  • name: Name of the listing.
  • host_id: Airbnb's unique identifier for the host.
  • host_name: Name of the host.
  • calculated_host_listings_count: The number of listings the host has.
  • neighbourhood_cleansed: The neighbourhood as geocoded using the latitude and longitude against neighborhoods as defined by open or public digital shapefiles.
  • latitude: Uses the World Geodetic System (WGS84) projection for latitude and longitude.
  • longitude: Uses the World Geodetic System (WGS84) projection for latitude and longitude.
  • room_type: Entire place, Private room, Shared room, Hotel room.
  • price: daily price in local currency.
  • minimum_nights: minimum number of night stay for the listing.
  • maximum_nights: maximum number of night stay for the listing.
  • availability_365: avaliability_x. The availability of the listing x days in the future as determined by the calendar. Note a listing may not be available because it has been booked by a guest or blocked by the host.
  • number_of_reviews: The number of reviews the listing has.
  • number_of_reviews_ltm: The number of reviews the listing has (in the last 12 months).
  • reviews_per_month: The average number of reviews per month the listing has over the lifetime of the listing.
  • first_review: The date of the first/oldest review.
In [4]:
# Select variables and save them for further analysis
data = raw_data.loc[:,
    [
        "id",
        "name",
        "host_id",
        "host_name",
        "calculated_host_listings_count",
        "neighbourhood_cleansed",
        "latitude",
        "longitude",
        "room_type",
        "price",
        "minimum_nights",
        "maximum_nights",
        "availability_365",
        "number_of_reviews",
        "number_of_reviews_ltm",
        "reviews_per_month",
        "first_review",
    ],
].copy()
In [5]:
# Data overview
data.head()
Out[5]:
id name host_id host_name calculated_host_listings_count neighbourhood_cleansed latitude longitude room_type price minimum_nights maximum_nights availability_365 number_of_reviews number_of_reviews_ltm reviews_per_month first_review
0 312761 Spacious Central London Apartment by Hoxton Sq... 1608226 Pippa 1 Hackney 51.52704 -0.08129 Entire home/apt $160.00 9 180 81 122 26 0.86 2012-07-12
1 13913 Holiday London DB Room Let-on going 54730 Alina 3 Islington 51.56861 -0.11270 Private room $65.00 1 29 351 41 1 0.25 2010-08-18
2 15400 Bright Chelsea Apartment. Chelsea! 60302 Philippa 1 Kensington and Chelsea 51.48780 -0.16813 Entire home/apt $120.00 4 30 88 94 2 0.54 2009-12-21
3 159736 A double Room 5mins from King's College Hospital 766056 Trevor 4 Lambeth 51.46788 -0.09993 Private room $65.00 4 96 268 96 1 0.62 2011-07-16
4 165336 Charming Flat in Notting Hill 761400 Nathan 1 Kensington and Chelsea 51.51735 -0.21076 Entire home/apt $100.00 1 14 3 237 25 1.57 2011-10-16
In [6]:
# Show the size of the data and check duplicate rows
[rowCount, coloumCount] = data.shape
print(f"the number of rows: {rowCount}")
print(f"the number of columns: {coloumCount}")
print(f"the number of duplicate rows: {data.duplicated().sum()}")

the number of rows: 90852
the number of columns: 17
the number of duplicate rows: 0
In [7]:
# Check if the `calculated_host_listings_count` is equal to the count of distinct `host_id`
ds1 = data["host_id"].value_counts().reset_index()
ds2 = (
    data.groupby("host_id")
    .aggregate({"calculated_host_listings_count": "first"})
    .sort_values(by="calculated_host_listings_count", ascending=False)
    .reset_index()
)
display(ds1.head())
display(ds2.head())
ds3 = pd.merge(ds1, ds2, on="host_id", how="outer")
ds3["diff"] = ds3["count"] - ds3["calculated_host_listings_count"]
print(f"the difference numbers: {ds3['diff'].sum(skipna=False)}")
host_id count
0 129230780 558
1 314162972 412
2 33889201 378
3 1432477 312
4 28820321 268
host_id calculated_host_listings_count
0 129230780 558
1 314162972 412
2 33889201 378
3 1432477 312
4 28820321 268 
the difference numbers: 0

Main Findings:

  • The calculated_host_listings_count is equal to the count of distinct host_id
  • Upon examination, no apparent errors were identified.
In [8]:
# Count the missing values and calculate the percentage
missingDetail = pd.DataFrame({"missing_count": data.isna().sum()})
missingDetail["missing_%"] = (missingDetail["missing_count"] / rowCount) * 100
print(missingDetail)

                                missing_count  missing_%
id                                          0   0.000000
name                                        0   0.000000
host_id                                     0   0.000000
host_name                                   5   0.005503
calculated_host_listings_count              0   0.000000
neighbourhood_cleansed                      0   0.000000
latitude                                    0   0.000000
longitude                                   0   0.000000
room_type                                   0   0.000000
price                                   32967  36.286488
minimum_nights                              0   0.000000
maximum_nights                              0   0.000000
availability_365                            0   0.000000
number_of_reviews                           0   0.000000
number_of_reviews_ltm                       0   0.000000
reviews_per_month                       24983  27.498569
first_review                            24983  27.498569

Main Findings:

  • There are about 36% of missing values in the variable price.
  • About 27% of listings do not have first_review and reviews_per_month.
  • It is worth to explore more on these variables.
In [9]:
# Explore missing values in `price`
data[data["price"].isna()]
Out[9]:
id name host_id host_name calculated_host_listings_count neighbourhood_cleansed latitude longitude room_type price minimum_nights maximum_nights availability_365 number_of_reviews number_of_reviews_ltm reviews_per_month first_review
5 313710 Pretty Home Kensal Green NW10 1 bed 1612623 Alex 1 Brent 51.533470 -0.232920 Entire home/apt NaN 2 14 0 10 0 0.07 2012-05-01
6 168359 Stunning 2 Bed Apartment in Elephant & Castle 648725 Michele 1 Southwark 51.491850 -0.088230 Entire home/apt NaN 2 1125 0 9 0 0.06 2011-07-23
8 24328 Battersea live/work artist house, garden communal 41759 Joe 1 Wandsworth 51.470720 -0.162660 Entire home/apt NaN 2 1125 0 94 0 0.58 2010-11-15
11 170702 A Double Room with River Views 814004 Marie 1 Tower Hamlets 51.496860 -0.026270 Private room NaN 3 365 0 135 0 0.88 2011-08-01
13 314985 Room in Artistic house, nr Olympics 1617885 Roger 1 Newham 51.526260 0.029040 Private room NaN 2 7 0 6 0 0.05 2013-10-13
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
87602 1091820475825413494 Fantastic 2 bedroom apartment in Surbiton 9063235 Executive Roomspace 101 Kingston upon Thames 51.390064 -0.302473 Entire home/apt NaN 1 365 26 0 0 NaN NaN
87636 1093296855207837501 Cozy and spacious flat 104544556 Angie 1 Lambeth 51.445472 -0.123503 Entire home/apt NaN 3 365 127 0 0 NaN NaN
88004 1095441435477010989 Magical townhouse getaway in London 33561493 Leah 1 Westminster 51.526263 -0.203725 Entire home/apt NaN 2 365 7 3 3 3.00 2024-03-09
88090 1096451917769415868 Jochebed House|Brixton Centre|Spacious|LongTerm 229912595 Nicole 5 Lambeth 51.455206 -0.116343 Entire home/apt NaN 3 365 170 0 0 NaN NaN
88740 1100946494095204584 Terrace in Brixton/ Clapham 553929117 Roland 1 Lambeth 51.455054 -0.124390 Entire home/apt NaN 1 365 92 0 0 NaN NaN

32967 rows × 17 columns

Main Findings:

  • From the above data, it can be seen that the data provide useful information even if prices are missing.
  • At the stage of EDA, they should not be removed.
In [10]:
# Explore missing values in `first_review` (`reviews_per_month`)
data[data["first_review"].isna()]
Out[10]:
id name host_id host_name calculated_host_listings_count neighbourhood_cleansed latitude longitude room_type price minimum_nights maximum_nights availability_365 number_of_reviews number_of_reviews_ltm reviews_per_month first_review
9 170524 STUNNING APT IN ST JAMES 194769 D 4 Westminster 51.506120 -0.140290 Entire home/apt $1,300.00 14 730 365 0 0 NaN NaN
35 318986 Central London flat for Olympics 1637212 Apprameya 1 Kensington and Chelsea 51.491130 -0.194820 Entire home/apt NaN 7 21 0 0 0 NaN NaN
45 42692 Fabulous flat w garden and bkfst! 186510 Shelley 1 Hammersmith and Fulham 51.508220 -0.215620 Private room NaN 1 14 0 0 0 NaN NaN
49 44384 DOUBLE ROOM IN A PENTHOUSE APARTMEN 194769 D 4 Barnet 51.597900 -0.243270 Private room $43.00 30 365 365 0 0 NaN NaN
56 324055 worth to stay.you will never regret 1664001 Ganesan 1 Newham 51.553110 0.022730 Private room NaN 150 365 0 0 0 NaN NaN
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
90847 1115272743905612628 Primrose Hill Studio #25 565833376 Henna 48 Bexley 51.502721 0.147342 Entire home/apt $225.00 1 365 268 0 0 NaN NaN
90848 1115272767893608505 Primrose Hill Studio #27 565833376 Henna 48 Bexley 51.504134 0.148848 Entire home/apt $225.00 1 365 268 0 0 NaN NaN
90849 1115285644506865913 Quad Bedroom with External Bathroom 444801189 The Chapter Hotels 33 Westminster 51.506404 -0.148199 Private room $314.00 1 365 363 0 0 NaN NaN
90850 1115338006572763275 Grosvenor Collection 514234035 Joe 52 Westminster 51.513649 -0.161906 Entire home/apt $610.00 1 45 347 0 0 NaN NaN
90851 1115347885713265376 Comfy Home - Wood Green 215155525 Mohamed 2 Haringey 51.600825 -0.104080 Entire home/apt $150.00 2 365 303 0 0 NaN NaN

24983 rows × 17 columns

Main Findings:

  • The data provide useful information even if first_review and reviews_per_month are missing.
  • There may be missing values because some customers do not leave any reviews on the listings.
  • At the stage of EDA, they should not be removed.
In [11]:
# Explore missing values in `host_name`
data[data["host_name"].isna()]
Out[11]:
id name host_id host_name calculated_host_listings_count neighbourhood_cleansed latitude longitude room_type price minimum_nights maximum_nights availability_365 number_of_reviews number_of_reviews_ltm reviews_per_month first_review
3927 5811550 large room in Shoreditch 8317501 NaN 1 Tower Hamlets 51.52512 -0.06566 Private room NaN 1 1125 0 0 0 NaN NaN
5081 7007873 Victoria / Pimlico 22047056 NaN 1 Westminster 51.49459 -0.13414 Private room NaN 8 1125 0 0 0 NaN NaN
5688 7595146 Nice room in near Canary wharf 39828462 NaN 1 Tower Hamlets 51.48730 -0.01428 Private room NaN 1 1125 0 0 0 NaN NaN
6220 8149344 LUXURIOUS SUITE IN HISTORIC HOUSE 43023101 NaN 1 Waltham Forest 51.63272 0.00607 Private room NaN 7 345 0 0 0 NaN NaN
6495 8511150 large room in camden 44815642 NaN 1 Camden 51.53744 -0.13965 Private room NaN 1 1125 0 0 0 NaN NaN

Main Findings:

  • There are 5 missing values simultaneously presenting in host_name ,price,reviews_per_month,and first_review.
  • At the stage of EDA, these missing values will not affect the analysis and should not be removed.
In [12]:
# Data summary
data.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 90852 entries, 0 to 90851
Data columns (total 17 columns):
 #   Column                          Non-Null Count  Dtype  
---  ------                          --------------  -----  
 0   id                              90852 non-null  int64  
 1   name                            90852 non-null  object 
 2   host_id                         90852 non-null  int64  
 3   host_name                       90847 non-null  object 
 4   calculated_host_listings_count  90852 non-null  int64  
 5   neighbourhood_cleansed          90852 non-null  object 
 6   latitude                        90852 non-null  float64
 7   longitude                       90852 non-null  float64
 8   room_type                       90852 non-null  object 
 9   price                           57885 non-null  object 
 10  minimum_nights                  90852 non-null  int64  
 11  maximum_nights                  90852 non-null  int64  
 12  availability_365                90852 non-null  int64  
 13  number_of_reviews               90852 non-null  int64  
 14  number_of_reviews_ltm           90852 non-null  int64  
 15  reviews_per_month               65869 non-null  float64
 16  first_review                    65869 non-null  object 
dtypes: float64(3), int64(8), object(6)
memory usage: 11.8+ MB
In [13]:
# Convert data type of `price` to float and `first_review` to datetime
data["price"] = data["price"].str.replace("[^-.0-9]", "", regex=True).astype(float)
data["first_review"] = pd.to_datetime(data["first_review"])
print(f"data type of price: {data['price'].dtypes}")
print(f"data type of first_review: {data['first_review'].dtypes}")

data type of price: float64
data type of first_review: datetime64[ns]
In [14]:
# Descriptive statistics on meaningful variables
data[
    [
        "calculated_host_listings_count",
        "price",
        "minimum_nights",
        "maximum_nights",
        "availability_365",
        "number_of_reviews",
        "number_of_reviews_ltm",
        "reviews_per_month",
    ]
].describe()
Out[14]:
calculated_host_listings_count price minimum_nights maximum_nights availability_365 number_of_reviews number_of_reviews_ltm reviews_per_month
count 90852.000000 57885.000000 90852.000000 9.085200e+04 90852.000000 90852.00000 90852.000000 65869.000000
mean 18.495927 180.275944 5.418747 6.486027e+03 124.256164 17.81132 5.488531 0.905957
std 65.205497 434.505248 22.099520 1.741865e+06 130.755632 42.88319 11.656508 1.195357
min 1.000000 0.000000 1.000000 1.000000e+00 0.000000 0.00000 0.000000 0.010000
25% 1.000000 74.000000 1.000000 6.000000e+01 0.000000 0.00000 0.000000 0.160000
50% 2.000000 125.000000 2.000000 3.650000e+02 80.000000 4.00000 1.000000 0.490000
75% 6.000000 200.000000 4.000000 1.125000e+03 249.000000 16.00000 6.000000 1.140000
max 558.000000 53588.000000 1125.000000 5.248556e+08 365.000000 1672.00000 475.000000 32.260000

Main Findings:

  • The minimum price is 0, and the highest number of maximum_nights exceeds 524 million, which necessitates further investigation.
  • The data are heavily skewed.
In [15]:
# Investigate the variable `price`
data.sort_values(by="price", ascending=True).head()
Out[15]:
id name host_id host_name calculated_host_listings_count neighbourhood_cleansed latitude longitude room_type price minimum_nights maximum_nights availability_365 number_of_reviews number_of_reviews_ltm reviews_per_month first_review
40878 49765360 Private room by Spitalfields Market 3010498 Michael 2 Tower Hamlets 51.515915 -0.073669 Private room 0.0 1 6 6 2 2 0.30 2023-09-06
35860 41155199 Large private room in Shoreditch apartment 3010498 Michael 2 Tower Hamlets 51.525840 -0.068670 Private room 1.0 30 1125 351 1 0 0.02 2020-08-15
87652 1093343136399687490 Double Bedroom in Luxury Apartment 100672427 Adam 1 Lambeth 51.474950 -0.108340 Private room 8.0 2 365 178 5 5 5.00 2024-02-24
72031 959968164600589433 Luxury Urban Cabin retreat 104056862 Cyprian 2 Sutton 51.352750 -0.176380 Entire home/apt 9.0 2 21 0 0 0 NaN NaT
66713 914539486714415414 Comfy room in central London 519672586 Natalia 1 Islington 51.526608 -0.103219 Private room 9.0 2 6 27 38 38 4.10 2023-06-18

Main Findings:

  • There is only 1 room with a 0 price, which may suggest that the room is conditional on some unknown factors for being offered for free.
  • The same host also offers a room at a cheaper price.
  • Therefore, it is not necessary to remove the data at this stage.
In [16]:
# Investigate the variable `maximum_nights`
data.sort_values(by="maximum_nights", ascending=False).head(5)
Out[16]:
id name host_id host_name calculated_host_listings_count neighbourhood_cleansed latitude longitude room_type price minimum_nights maximum_nights availability_365 number_of_reviews number_of_reviews_ltm reviews_per_month first_review
6074 7878442 Small single bedroom 41528394 Michael 3 Merton 51.40544 -0.20928 Private room 28.0 1 524855552 309 281 45 2.72 2015-09-27
12992 15695715 lovely double room in house, honor oak/foresthill 25655886 Josh 1 Lewisham 51.44673 -0.05076 Private room NaN 1 10000000 0 1 0 0.01 2016-11-15
15131 17877540 London Bridge Single Room 170pw 89593642 珀 1 Southwark 51.50335 -0.09031 Private room NaN 9 9000000 0 0 0 NaN NaT
173 270600 Patio Apartment in London (Twickenham) 1416605 Emma 2 Richmond upon Thames 51.44311 -0.33245 Entire home/apt 80.0 4 9011 158 79 9 0.61 2013-07-17
4649 6622730 Lovely DOUBLE ROOM in Hackney! 20418398 Silvia 3 Hackney 51.55226 -0.06549 Private room NaN 3 2000 0 11 0 0.10 2015-06-08

Main Findings:

  • There are 4 rooms that can be lived in for more than 20 years.
  • Compared to others, the 'maximum_nights' values in the first 4 rows of the data seem to be unusual.
  • These 4 rows will be removed.
In [17]:
# Before removing the abnormal data, it is necessary to recalculate the values for the variable `calculated_host_listings_count`.
recalculated = (
    data.loc[data["maximum_nights"] > 9000, "host_id"].value_counts().reset_index()
)

for id, val in zip(recalculated["host_id"], recalculated["count"]):
    data.loc[data["host_id"] == id, "calculated_host_listings_count"] = (
        data.loc[data["host_id"] == id, "calculated_host_listings_count"] - val
    )

# Remove the abnormal data
data = data[data["maximum_nights"] < 9000].reset_index(drop=True)
data.sort_values(by="maximum_nights", ascending=False).head()
Out[17]:
id name host_id host_name calculated_host_listings_count neighbourhood_cleansed latitude longitude room_type price minimum_nights maximum_nights availability_365 number_of_reviews number_of_reviews_ltm reviews_per_month first_review
4648 6622730 Lovely DOUBLE ROOM in Hackney! 20418398 Silvia 3 Hackney 51.55226 -0.06549 Private room NaN 3 2000 0 11 0 0.10 2015-06-08
6248 8168705 Romantic Double room in Arty flat in Hackney 20418398 Silvia 3 Hackney 51.55353 -0.06593 Private room NaN 3 2000 0 12 0 0.12 2015-09-14
1986 2836575 Beautiful room in period house 13709501 Faith And Tony 1 Islington 51.56041 -0.09957 Private room 48.0 2 1444 1 58 0 0.49 2014-07-01
28787 32293161 Clarkson Double room 3 31870202 Juhel 17 Tower Hamlets 51.52794 -0.06004 Private room NaN 1 1125 0 40 0 0.64 2019-02-14
28791 32154993 Nice flat all to yourselves - 10 min walk to tube 27992377 Paul 1 Waltham Forest 51.56412 -0.01452 Entire home/apt NaN 5 1125 0 8 0 0.13 2019-04-27
In [18]:
# Cross-check the data
print(f"observations: {len(data['host_id'])}")
print(f"observations: {data['host_id'].value_counts().sum()}")
obsCheck = (
    data.groupby("host_id")
    .aggregate({"calculated_host_listings_count": "first"})
    .sort_values(by="calculated_host_listings_count", ascending=False)
    .reset_index()
)
print(f"observations: {sum(obsCheck.calculated_host_listings_count)}")

observations: 90848
observations: 90848
observations: 90848

Exploratory data analysis ¶

In [19]:
# Data summary
data.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 90848 entries, 0 to 90847
Data columns (total 17 columns):
 #   Column                          Non-Null Count  Dtype         
---  ------                          --------------  -----         
 0   id                              90848 non-null  int64         
 1   name                            90848 non-null  object        
 2   host_id                         90848 non-null  int64         
 3   host_name                       90843 non-null  object        
 4   calculated_host_listings_count  90848 non-null  int64         
 5   neighbourhood_cleansed          90848 non-null  object        
 6   latitude                        90848 non-null  float64       
 7   longitude                       90848 non-null  float64       
 8   room_type                       90848 non-null  object        
 9   price                           57883 non-null  float64       
 10  minimum_nights                  90848 non-null  int64         
 11  maximum_nights                  90848 non-null  int64         
 12  availability_365                90848 non-null  int64         
 13  number_of_reviews               90848 non-null  int64         
 14  number_of_reviews_ltm           90848 non-null  int64         
 15  reviews_per_month               65866 non-null  float64       
 16  first_review                    65866 non-null  datetime64[ns]
dtypes: datetime64[ns](1), float64(4), int64(8), object(4)
memory usage: 11.8+ MB
In [20]:
# Locations overview
fig = px.density_mapbox(
    data,
    lat="latitude",
    lon="longitude",
    hover_name="name",
    hover_data="price",
    radius=2,
    color_continuous_scale=[
        [0.0, "green"],
        [0.25, "yellow"],
        [0.5, "blue"],
        [0.75, "purple"],
        [1, "red"],
    ],
    opacity=0.5,
    width=800,
    height=600,
)
fig.update_layout(mapbox_style="open-street-map")
fig.show()

Main Findings:

  • The Airbnb services cover most areas within London.
In [21]:
# Boxplot on meaningful variables
numericVariables = [
    "calculated_host_listings_count",
    "price",
    "minimum_nights",
    "maximum_nights",
    "availability_365",
    "number_of_reviews",
    "number_of_reviews_ltm",
    "reviews_per_month",
]
numericData = data[numericVariables].copy()
[fig, axes] = plt.subplots(3, 3)
for val, axe in zip(numericVariables, axes.flat):
    sns.boxplot(ax=axe, data=numericData, x=val)
    axe.set_title(val, fontsize=10)
    axe.set_xlabel("")
    axe.set_xticks(np.linspace(min(numericData[val]), max(numericData[val]), 5))
    axe.tick_params(axis="both", labelsize=7)
axes[2, 2].axis("off")
fig.tight_layout()
No description has been provided for this image

Main Findings:

  • It is obvious that the data are heavily skewed.
  • A host may have many listings.
  • Some rooms can be very expensive.
  • Some rooms are quite popular, while others are not.
In [22]:
# Explore the room types
roomCount = data["room_type"].value_counts().reset_index()
fig = px.pie(roomCount, values="count", names="room_type")
fig.show()

Main Findings:

  • Airbnb listings are primarily composed of entire homes or apartments, as well as private rooms.
In [23]:
# Explore the number of single and multi-listings
print(
    f"There are about {data['host_id'].nunique()} hosts and {len(data['host_id'])} listings in the market."
)
listCount = data["host_id"].value_counts()
print(f"Multi-listings: {listCount[listCount>1].sum()}")
print(f"Single-listings: {listCount[listCount==1].sum()}")

# Explore the number of listings among the top ten hosts
topHosts = (
    data.groupby("host_id")
    .aggregate({"calculated_host_listings_count": "first"})
    .sort_values(by="calculated_host_listings_count", ascending=False)
    .head(10)
    .reset_index()
)
topHosts["calculated_host_listings_count%"] = (
    topHosts["calculated_host_listings_count"] / len(data["host_id"]) * 100
)

display(topHosts)

# Explore the number of listings among the top ten areas
topAreas = data["neighbourhood_cleansed"].value_counts().head(10).reset_index()
topAreas["count%"] = topAreas["count"] / len(data["host_id"]) * 100
display(topAreas)

There are about 55035 hosts and 90848 listings in the market.
Multi-listings: 46173
Single-listings: 44675
host_id calculated_host_listings_count calculated_host_listings_count%
0 129230780 558 0.614213
1 314162972 412 0.453505
2 33889201 378 0.416080
3 1432477 312 0.343431
4 28820321 268 0.294998
5 258154594 212 0.233357
6 48165024 201 0.221249
7 156158778 201 0.221249
8 269308503 188 0.206939
9 439074505 174 0.191529
neighbourhood_cleansed count count%
0 Westminster 10246 11.278179
1 Tower Hamlets 7256 7.986967
2 Hackney 6279 6.911545
3 Camden 5948 6.547200
4 Kensington and Chelsea 5944 6.542797
5 Southwark 5083 5.595060
6 Lambeth 4900 5.393625
7 Islington 4873 5.363905
8 Wandsworth 4681 5.152563
9 Hammersmith and Fulham 3897 4.289583

Main Findings:

  • Airbnb in London consists of around 55,035 hosts and 90,848 listings.
  • Approximately half of the hosts possess more than one listing.
  • The top ten hosts individually have more than 150 listings.
  • The most popular area is Westminster, accounting for more than 11% of the listings.
In [24]:
# Explore price ranges and the number of listings
bins = np.arange(0, 1001, 100)
bins = np.ceil(np.append(bins, max(data.price) + 1))
data["priceBins"] = pd.cut(data["price"], bins, right=False)
priceStat = (
    data.groupby("priceBins")
    .aggregate(priceBinCount=("priceBins", "count"))
    .reset_index()
)
priceStat["priceBinCount%"] = priceStat["priceBinCount"] / sum(priceStat["priceBinCount"])

# Visualize price ranges and the number of listings
[fig, axes] = plt.subplots(1, 2)

ax = sns.barplot(ax=axes[0], data=priceStat, x="priceBins", y="priceBinCount")
ax.bar_label(ax.containers[0], fontsize=7)
axes[0].tick_params(axis="x", rotation=55, labelsize=7)

theLegend = (
    np.round(priceStat["priceBinCount%"] * 100, 1).astype(str)
    + "% in "
    + priceStat["priceBins"].astype(str)
)
axes[1].pie(priceStat["priceBinCount"])
axes[1].legend(theLegend, bbox_to_anchor=(1, 1))

plt.sca(axes[0])
plt.xticks(ha="right")
fig.suptitle(
    "Price ranges, the numbers of listings and the respective percentages of total listings",
    ha="center",
    fontsize=15,
)
plt.show()
No description has been provided for this image

Main Findings:

  • At least 95% of the market is occupied by rooms with prices lower than 500 pounds per night.
  • It is worth mentioning that the luxury market, with prices beyond 1000 pounds, has about 1% market share.
In [25]:
# locations of those luxury rooms
data1000 = data.loc[data["price"] >= 1000, ["price", "name", "latitude", "longitude"]]
fig = px.scatter_mapbox(
    data1000,
    lat="latitude",
    lon="longitude",
    hover_name="name",
    hover_data="price",
    width=800,
    height=600,
)
fig.update_layout(mapbox_style="open-street-map")
fig.show()

Main Findings:

  • The luxury rooms are spread across a wide range of locations in London.
In [26]:
# Explore price ranges [0,500) and the room types
price500 = data.loc[data["price"] < 500, ["room_type", "price"]]
sns.violinplot(data=price500, x="room_type", y="price", palette="Set2")
plt.yticks(np.arange(0, 600, 50))
plt.ylim(0, 600)
plt.grid()
plt.show()
No description has been provided for this image
In [27]:
# Conduct t-test
groupPrice = data.pivot(columns=["room_type"], values="price")

print("t-test for the means of 'Entire home/apt' and 'Hotel room' :")
print(
    stats.ttest_ind(
        a=groupPrice["Entire home/apt"],
        b=groupPrice["Hotel room"],
        equal_var=False,
        nan_policy="omit",
    )
)

print("")

print("t-test for the means of 'Private room' and 'Shared room' :")
print(
    stats.ttest_ind(
        a=groupPrice["Private room"],
        b=groupPrice["Shared room"],
        equal_var=False,
        nan_policy="omit",
    )
)

print("")

print("t-test for the means of 'Private room' and 'Entire home/apt' :")
print(
    stats.ttest_ind(
        a=groupPrice["Private room"],
        b=groupPrice["Entire home/apt"],
        alternative="less",
        equal_var=False,
        nan_policy="omit",
    )
)

t-test for the means of 'Entire home/apt' and 'Hotel room' :
TtestResult(statistic=0.2684999449397016, pvalue=0.7887985760650547, df=114.28703319994048)

t-test for the means of 'Private room' and 'Shared room' :
TtestResult(statistic=-1.7477038883721987, pvalue=0.08154561337272741, df=297.90297671231235)

t-test for the means of 'Private room' and 'Entire home/apt' :
TtestResult(statistic=-35.48614166830611, pvalue=2.0250237641758515e-271, df=35836.973693694126)

Main Findings:

  • The pricing settings are similar between Entire home/apt and Hotel room, as well as between Private room and Shared room.
  • The prices of Private room are significantly less than those of Entire home/apt.
In [28]:
# Descriptive statistics on minimum_nights and maximum_nights
minimum_nights = (
    data.groupby("room_type")["minimum_nights"]
    .describe(percentiles=[0.05, 0.25, 0.50, 0.75, 0.95])
    .reset_index()
)
minimum_nights.rename(columns={"room_type": "room_type:minimum_nights"}, inplace=True)

maximum_nights = (
    data.groupby("room_type")["maximum_nights"]
    .describe(percentiles=[0.05, 0.25, 0.50, 0.75, 0.95])
    .reset_index()
)
maximum_nights.rename(columns={"room_type": "room_type:maximum_nights"}, inplace=True)

display(minimum_nights)
display(maximum_nights)

# Visualize room type and minimum/maximum nights
[fig, axes] = plt.subplots(1, 2, figsize=(10, 5))
axes[0].scatter(data=data, x="room_type", y="minimum_nights", s=60, alpha=0.01)
axes[0].set_title("miminum_nights")
axes[1].scatter(data=data, x="room_type", y="maximum_nights", s=60, alpha=0.01)
axes[1].set_title("maxinum_nights")

fig.suptitle("Room type and minimum/maximum nights")
fig.tight_layout()
room_type:minimum_nights count mean std min 5% 25% 50% 75% 95% max
0 Entire home/apt 57260.0 5.968530 19.793913 1.0 1.0 2.0 3.0 4.0 20.00 1124.0
1 Hotel room 181.0 2.077348 3.163083 1.0 1.0 1.0 1.0 3.0 3.00 30.0
2 Private room 32948.0 4.493626 25.572087 1.0 1.0 1.0 2.0 3.0 11.65 1125.0
3 Shared room 459.0 4.572985 27.318128 1.0 1.0 1.0 1.0 2.0 7.10 365.0
room_type:maximum_nights count mean std min 5% 25% 50% 75% 95% max
0 Entire home/apt 57260.0 510.980335 436.777168 1.0 14.0 90.0 365.0 1125.0 1125.0 1125.0
1 Hotel room 181.0 819.453039 469.031039 7.0 30.0 91.0 1125.0 1125.0 1125.0 1125.0
2 Private room 32948.0 477.976144 466.183141 1.0 6.0 30.0 365.0 1125.0 1125.0 2000.0
3 Shared room 459.0 541.405229 484.904422 1.0 3.0 26.0 365.0 1125.0 1125.0 1125.0
No description has been provided for this image

Main Findings:

  • The fluctuations in both minimum_nights and maximum_nights are large.
  • Entire home/apt and Private room are similar in terms of minimum or maximum number of nights stay.
    • Only 5% of minimum_nights are greater than 20 in Entire home/apt , and 11 in Private room.
  • The services offered are primarily designed for short-term rental arrangements.
  • At least 50% of the Hotel rooms have a maximum_nights value greater than 1125.
    • Compared to other rental services, hotel rooms are more likely to cater to guests seeking longer-term rental options.
    • Individuals traveling for business or other purposes may prefer to stay in a hotel room as hotel rooms provide a level of service and hospitality associated with traditional hotels.
In [29]:
# Explore the correlation between variables
theVariables = [
    "calculated_host_listings_count",
    "price",
    "minimum_nights",
    "maximum_nights",
    "availability_365",
    "number_of_reviews",
    "number_of_reviews_ltm",
    "reviews_per_month",
    "latitude",
    "longitude",
]
corrVar = data[theVariables]
plt.figure(figsize=(10, 5))
coef = corrVar.corr()
sns.heatmap(coef, annot=True, annot_kws={"fontsize": 8}, cmap="crest", vmin=-1, vmax=1)
plt.xticks(rotation=20, ha="right")
plt.show()
No description has been provided for this image

Main Findings:

  • The variables are not highly correlated with each other except reviews.
  • The number of reviews the listing has in the last 12 months(number_of_reviews_ltm) is highly correlated with number_of_reviews and reviews_per_month.
    • In order to avoid multicollinearity, the variable number_of_reviews_ltm will be the only one included in the model.
In [30]:
# Estimate the minimum nights booked, the minimum price per night and the minimum income for the past 12 months
# The data will exclude listings without price information
# The number of reviews for each listing during the past 12 months is used as a factor in the analysis
estData = data.loc[
    ((data["price"].notna()) & (data["price"] != 0)),
    ["minimum_nights", "number_of_reviews_ltm", "price", "availability_365"],
]
minimum_total_nights = (
    estData["minimum_nights"] * estData["number_of_reviews_ltm"]
).sum(skipna=False)
minimum_total_income = (
    estData["minimum_nights"] * estData["number_of_reviews_ltm"] * estData["price"]
).sum(skipna=False)

minimum_nights_booked = minimum_total_nights / len(estData)
minimum_price_per_night = minimum_total_income / minimum_total_nights
minimum_income = minimum_total_income / len(estData)

print(f"minimum_nights_booked: {minimum_nights_booked:.0f}")
print(f"minimum_price_per_night:{minimum_price_per_night:.0f}")
print(f"minimum_income:{minimum_income:.0f}")
print(
    f"average available days for booking in a year:{estData['availability_365'].mean(skipna=False):.0f}"
)

minimum_nights_booked: 21
minimum_price_per_night:148
minimum_income:3172
average available days for booking in a year:187

Main Findings:

  • Over the past 12 months, the average minimum nights booked was about 21 nights, with the average minimum price per night being around 148 pounds. Consequently, the average minimum income was about 3172 pounds.
  • The average number of days available for booking in a year is 187. This could be due to the property being booked by guests or blocked by the host.
  • The minimum_nights does not accurately reflect the actual stays, and the number_of_reviews_ltm also does not indicate the actual number of orders. Decisions relying on these metrics demand careful deliberation.

Model estimation and prediction ¶

Data preparation for modeling ¶

In [31]:
# Ensure robust estimation and prediction, it is necessary to remove missing values and handle outliers
# Prices lower than 8 pounds will be excluded
mdlData = data.loc[
    ((data["price"].notna()) & (data["price"] >= 8)),
    [
        "calculated_host_listings_count",
        "room_type",
        "minimum_nights",
        "maximum_nights",
        "availability_365",
        "number_of_reviews_ltm",
        "price",
        "latitude",
        "longitude",
    ],
]
# Create dummy variables from `room_type`
mdlData = pd.get_dummies(
    mdlData, columns=["room_type"], prefix="", prefix_sep="", dtype=int
)
mdlData.drop(["Hotel room"], axis=1, inplace=True)
In [32]:
# Functions used to detect outliers
def outliersNumber_IQR(vec):
    pct25 = vec.quantile(0.25)
    pct75 = vec.quantile(0.75)
    iqr = pct75 - pct25
    upperLimit = pct75 + 1.5 * iqr
    lowerLimit = pct25 - 1.5 * iqr
    outliersNumber = sum((vec > upperLimit) | (vec < lowerLimit))
    outlierIndex = vec[(vec > upperLimit) | (vec < lowerLimit)].index
    return outliersNumber, outlierIndex


def outliersNumber_Std(vec):
    upperLimit = vec.mean() + 3 * vec.std()
    lowerLimit = vec.mean() - 3 * vec.std()
    outliersNumber = sum((vec > upperLimit) | (vec < lowerLimit))
    outlierIndex = vec[(vec > upperLimit) | (vec < lowerLimit)].index
    return outliersNumber, outlierIndex
In [33]:
# Count the number of outliers
print("the number of outliers based on 1.5 IQR >>")
for var in mdlData.columns:
    [outliersNumber, _] = outliersNumber_IQR(mdlData[var])
    print(f"{var}: {outliersNumber}")

the number of outliers based on 1.5 IQR >>
calculated_host_listings_count: 8297
minimum_nights: 4518
maximum_nights: 0
availability_365: 0
number_of_reviews_ltm: 4606
price: 3874
latitude: 2778
longitude: 2163
Entire home/apt: 0
Private room: 0
Shared room: 293
In [34]:
# Count the number of outliers
print("the number of outliers based on 3std >>")
for var in mdlData.columns:
    [outliersNumber, _] = outliersNumber_Std(mdlData[var])
    print(f"{var}: {outliersNumber}")

the number of outliers based on 3std >>
calculated_host_listings_count: 1497
minimum_nights: 740
maximum_nights: 0
availability_365: 0
number_of_reviews_ltm: 1462
price: 271
latitude: 445
longitude: 644
Entire home/apt: 0
Private room: 0
Shared room: 293
In [35]:
# Treating important values as outliers and removing them will change the meaning of the data
# Outliers in this dataset will be identified exclusively within the `price` variable
[numIQR, idxIQR] = outliersNumber_IQR(mdlData["price"])
[numStd, idxStd] = outliersNumber_Std(mdlData["price"])
print("outliers based on 1.5 IQR threshold:")
print(mdlData.loc[idxIQR, "price"].sort_values())
print("")
print("outliers based on 3std threshold:")
print(mdlData.loc[idxStd, "price"].sort_values())
mdlDataClean = mdlData.drop(idxStd)

outliers based on 1.5 IQR threshold:
82931      390.0
85729      390.0
51646      390.0
62830      390.0
67273      390.0
          ...   
70132    12000.0
42717    20000.0
7671     25000.0
27139    50000.0
10490    53588.0
Name: price, Length: 3874, dtype: float64

outliers based on 3std threshold:
67931     1486.0
22987     1486.0
59776     1488.0
35479     1490.0
84024     1492.0
          ...   
75204    12000.0
42717    20000.0
7671     25000.0
27139    50000.0
10490    53588.0
Name: price, Length: 271, dtype: float64

Main Findings:

  • When using the 1.5 IQR rule to detect outliers in price, any prices exceeding 389.9 will be removed. In contrast, the rule of 3 standard deviations (3std) sets the price threshold at 1486.
  • Since at least 95% of the market consists of rooms priced under 500 pounds per night, the rule of 3 standard deviations will be applied for outlier detection.
In [36]:
# Summary of the cleaned data
mdlDataClean.reset_index(drop=True, inplace=True)
mdlDataClean.info()
mdlDataClean.describe()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 57610 entries, 0 to 57609
Data columns (total 11 columns):
 #   Column                          Non-Null Count  Dtype  
---  ------                          --------------  -----  
 0   calculated_host_listings_count  57610 non-null  int64  
 1   minimum_nights                  57610 non-null  int64  
 2   maximum_nights                  57610 non-null  int64  
 3   availability_365                57610 non-null  int64  
 4   number_of_reviews_ltm           57610 non-null  int64  
 5   price                           57610 non-null  float64
 6   latitude                        57610 non-null  float64
 7   longitude                       57610 non-null  float64
 8   Entire home/apt                 57610 non-null  int32  
 9   Private room                    57610 non-null  int32  
 10  Shared room                     57610 non-null  int32  
dtypes: float64(3), int32(3), int64(5)
memory usage: 4.2 MB
Out[36]:
calculated_host_listings_count minimum_nights maximum_nights availability_365 number_of_reviews_ltm price latitude longitude Entire home/apt Private room Shared room
count 57610.000000 57610.00000 57610.000000 57610.000000 57610.000000 57610.000000 57610.000000 57610.000000 57610.000000 57610.000000 57610.000000
mean 17.902083 5.11899 459.362211 186.367540 7.861968 164.600660 51.509056 -0.129990 0.662125 0.330863 0.005069
std 53.520948 16.60028 405.091966 117.831492 13.563883 149.134619 0.049650 0.105326 0.472990 0.470528 0.071014
min 1.000000 1.00000 1.000000 0.000000 0.000000 8.000000 51.295937 -0.497800 0.000000 0.000000 0.000000
25% 1.000000 1.00000 90.000000 80.000000 0.000000 73.000000 51.484502 -0.192500 0.000000 0.000000 0.000000
50% 2.000000 2.00000 365.000000 180.000000 3.000000 124.000000 51.513033 -0.132971 1.000000 0.000000 0.000000
75% 10.000000 4.00000 730.000000 285.000000 10.000000 200.000000 51.537456 -0.068937 1.000000 1.000000 0.000000
max 558.000000 999.00000 1444.000000 365.000000 475.000000 1480.000000 51.681781 0.295731 1.000000 1.000000 1.000000

Estimation ¶

In [37]:
# Visualize dependent variable
[fig, axes] = plt.subplots(1, 2)
price = mdlDataClean["price"]
logPrice = np.log(price)
sns.histplot(ax=axes[0], data=price)
axes[0].set_title("price")
axes[0].set_xlabel("")
sns.histplot(ax=axes[1], data=logPrice)
axes[1].set_title("log price")
axes[1].set_xlabel("")
fig.tight_layout()
No description has been provided for this image
In [38]:
# Normalize data
X = mdlDataClean.drop(["price"], axis=1)
y = mdlDataClean["price"]
X_norm = X.copy()
X_norm.iloc[:, :-3] = (X_norm.iloc[:, :-3] - X_norm.iloc[:, :-3].mean()) / X_norm.iloc[:, :-3].std()

# Fit linear regression model
cX_norm = sm.add_constant(X_norm)
log_y = np.log(y)
lmModel = sm.OLS(log_y, cX_norm)
lmResult = lmModel.fit()
print(lmResult.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                  price   R-squared:                       0.432
Model:                            OLS   Adj. R-squared:                  0.432
Method:                 Least Squares   F-statistic:                     4379.
Date:                Wed, 10 Jul 2024   Prob (F-statistic):               0.00
Time:                        21:28:05   Log-Likelihood:                -47172.
No. Observations:               57610   AIC:                         9.437e+04
Df Residuals:                   57599   BIC:                         9.446e+04
Df Model:                          10                                         
Covariance Type:            nonrobust                                         
==================================================================================================
                                     coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------------------
const                              5.0847      0.052     97.944      0.000       4.983       5.186
calculated_host_listings_count     0.0293      0.002     12.197      0.000       0.025       0.034
minimum_nights                    -0.0135      0.002     -5.844      0.000      -0.018      -0.009
maximum_nights                     0.0134      0.002      5.625      0.000       0.009       0.018
availability_365                   0.0567      0.002     24.142      0.000       0.052       0.061
number_of_reviews_ltm             -0.0535      0.002    -22.976      0.000      -0.058      -0.049
latitude                          -0.0010      0.002     -0.426      0.670      -0.005       0.004
longitude                         -0.0373      0.002    -16.239      0.000      -0.042      -0.033
Entire home/apt                    0.0647      0.052      1.244      0.213      -0.037       0.167
Private room                      -0.9019      0.052    -17.314      0.000      -1.004      -0.800
Shared room                       -1.0067      0.061    -16.488      0.000      -1.126      -0.887
==============================================================================
Omnibus:                     5587.216   Durbin-Watson:                   1.918
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             9158.037
Skew:                           0.707   Prob(JB):                         0.00
Kurtosis:                       4.348   Cond. No.                         57.8
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

Main Findings:

  • Only about 43% of the variation in price is explained by the model.
  • All independent variables, except for Entire home/apt and latitude, are statistically significant at the 5% level.
  • The price in Entire home/apt overall is not significantly different from the average price, whereas prices for Private room and Shared room are significantly lower.

Prediction ¶

In [39]:
# Split the data into training and testing sets
[X_train, X_test, y_train, y_test] = train_test_split(
    X_norm, log_y, test_size=0.3, random_state=8
)

# Get shape of each training and testing set
X_train.shape, X_test.shape, y_train.shape, y_test.shape
Out[39]:
((40327, 10), (17283, 10), (40327,), (17283,))
In [40]:
# Build the models 
models = [
    ("linReg", LinearRegression()),
    ("KNN", KNeighborsRegressor()),
    ("treeReg", DecisionTreeRegressor(random_state=8)),
    ("rForest", RandomForestRegressor(n_jobs=-1, random_state=8)),
    ("NN", MLPRegressor(random_state=8)),
    ("XGBoost", XGBRegressor(objective="reg:squarederror")),
]
In [41]:
# Function to evaluate models
def modelEvaluation(models, X_train=None, y_train=None, X_test=None, y_test=None):
    resultTable = {}
    predValue = {}
    
    for modelName, model in models:
        timeBeg = time.time()
        model.fit(X_train, y_train)
        y_pred = model.predict(X_test)
        r2 = metrics.r2_score(y_test, y_pred)
        rmse = metrics.root_mean_squared_error(y_test, y_pred)
        mae = metrics.mean_absolute_error(y_test, y_pred)
        timeDur = time.time() - timeBeg
    
        resultTable.update({modelName: [r2, rmse, mae, timeDur]})
        predValue.update({modelName: np.exp(y_pred)})
    
    resultTable = pd.DataFrame(resultTable)
    resultTable.index = ["R_squared", "RMSE", "MAE", "model_time"]
    predValue = pd.DataFrame(predValue)
    predValue["actual"] = np.exp(y_test.reset_index(drop=True))
    
    print("models performance >>")
    display(resultTable.head())
    print("")
    print("predictions overview >>")
    display(predValue.head())
    
    return resultTable, predValue
In [42]:
# Function to visualize models performance
def modelVisualization(resultTable):
    modelNames = resultTable.columns
    [fig, axes] = plt.subplots(2, 2, figsize=(10, 8))
    axes[0, 0].bar(modelNames, resultTable.loc["R_squared"])
    axes[0, 0].set_title("R_squared")
    axes[0, 1].bar(modelNames, resultTable.loc["RMSE"])
    axes[0, 1].set_title("RMSE")
    axes[1, 0].bar(modelNames, resultTable.loc["MAE"])
    axes[1, 0].set_title("MAE")
    axes[1, 1].bar(modelNames, resultTable.loc["model_time"])
    axes[1, 1].set_title("model_time")
    fig.tight_layout()
In [43]:
# Evaluate models
[resultTable, predValue] = modelEvaluation(models,X_train=X_train, y_train=y_train, X_test=X_test, y_test=y_test)

models performance >>
linReg KNN treeReg rForest NN XGBoost
R_squared 0.428819 0.521496 0.240494 0.621761 0.541423 0.602591
RMSE 0.548291 0.501842 0.632252 0.446177 0.491282 0.457345
MAE 0.420852 0.378400 0.459068 0.331646 0.377680 0.345998
model_time 0.043476 1.865096 0.433664 4.603305 33.483443 0.334987 
predictions overview >>
linReg KNN treeReg rForest NN XGBoost actual
0 176.263925 471.278492 120.0 225.966673 220.851056 242.441010 190.0
1 181.782208 109.235393 160.0 146.441860 150.120065 127.212334 88.0
2 188.819067 835.473237 1343.0 1005.958684 494.427561 733.099426 818.0
3 193.325515 162.284003 176.0 243.125413 151.078490 183.241852 186.0
4 190.426565 261.645960 257.0 171.856864 176.556480 200.912277 280.0
In [44]:
#  Visualize models performance
modelVisualization(resultTable)
No description has been provided for this image
In [45]:
# Standardize the data based on RobustScaler
scaler = RobustScaler()

X_RobustScaler = X.copy()
X_RobustScaler.iloc[:, :-3] = scaler.fit_transform(X_RobustScaler.iloc[:, :-3])

# Split the data into training and testing sets
[X_train2, X_test2, y_train2, y_test2] = train_test_split(
    X_RobustScaler, log_y, test_size=0.3, random_state=8
)

# Get shape of each training and testing set
X_train2.shape, X_test2.shape, y_train2.shape, y_test2.shape
Out[45]:
((40327, 10), (17283, 10), (40327,), (17283,))
In [46]:
# Evaluate models and visualize models performance
[resultTable, predValue] = modelEvaluation(models,X_train=X_train2, y_train=y_train2, X_test=X_test2, y_test=y_test2)
modelVisualization(resultTable)

models performance >>
linReg KNN treeReg rForest NN XGBoost
R_squared 0.428819 0.524314 0.240472 0.621523 0.524427 0.602591
RMSE 0.548291 0.500362 0.632261 0.446318 0.500303 0.457345
MAE 0.420852 0.375185 0.459035 0.331739 0.387880 0.345998
model_time 0.017076 1.041927 0.386999 4.273219 18.431143 0.297456 
predictions overview >>
linReg KNN treeReg rForest NN XGBoost actual
0 176.263925 296.671976 120.0 222.680089 237.307924 242.441010 190.0
1 181.782208 91.504413 160.0 148.557711 156.914056 127.212334 88.0
2 188.819067 886.840392 1343.0 1003.907071 527.451897 733.099426 818.0
3 193.325515 281.182318 176.0 243.319430 145.773286 183.241852 186.0
4 190.426565 268.727692 257.0 170.414419 200.283560 200.912277 280.0
No description has been provided for this image

Main Findings:

  • The best model is the Random Forest.
  • Standardization of the data does not appear to enhance the model's predictive performance.

Hyperparameter tuning ¶

In [47]:
# Build models
modelsHyper = [
    ("elasticNet", ElasticNet()),
    ("KNN", KNeighborsRegressor()),
    ("treeReg", DecisionTreeRegressor(random_state=8)),
    ("rForest", RandomForestRegressor(n_jobs=-1, random_state=8)),
    ("NN", MLPRegressor(random_state=8)),
    ("XGBoost", XGBRegressor(objective="reg:squarederror")),
]
In [48]:
# Create a dictionary of hyperparameters to tune for each model
modelParam = {
    "elasticNet": {
        'alpha': [0, 0.5, 1, 2, 3], 
        'l1_ratio': [0, 0.25, 0.5, 0.75, 1]
    },
    "KNN": {
        "n_neighbors": [3, 5, 7], 
        "weights": ["uniform", "distance"]
    },
    "treeReg": {
        "max_depth": [10, None], 
        "min_samples_leaf": [1, 2, 3, 4, 5]
    },
    "rForest": {
        "max_features": [3, 4, 5],
        "n_estimators": [100, 130, 160],
        "min_samples_split": [2, 3, 4],
    },
    "NN": {
        "hidden_layer_sizes": [(100,), (50, 25)],
        "activation": ["identity", "logistic", "tanh", "relu"],
        "solver": ["lbfgs", "sgd", "adam"],
        "max_iter": [500],
    },
    "XGBoost": {
        "min_child_weight": [1, 2, 3, 4, 5],
        "learning_rate": [0.01, 0.05, 0.1, 0.2, 0.3],
        "n_estimators": [100, 300, 500],
    },
}

# Assign a set of scoring metrics to capture
scoring = ["r2", "neg_root_mean_squared_error", "neg_mean_absolute_error"]

# Examine the best model from GridSearchCV
modelObjects = {}
for modelName, model in modelsHyper:
    timeBeg = time.time()
    theSearch = GridSearchCV(
        model, modelParam[modelName], scoring=scoring, cv=5, refit="r2", n_jobs=-1
    )
    modelObjects[modelName] = theSearch.fit(X_train, y_train)
    timeDur = time.time() - timeBeg
    modelObjects[modelName + "Time"] = timeDur
In [49]:
# Function to extract scores from the GridSearchCV fit object
def estimationResult(modelObjects):
    theBestEstimators = {}
    theBestParameters = {}
    estimationCompare = {}
    modelNames = [v for v in modelObjects.keys() if not all(s in v for s in 'Time')]
    for modelName in modelNames:
        cv_results = pd.DataFrame(modelObjects[modelName].cv_results_)
        best_estimator_results = cv_results.iloc[cv_results['mean_test_r2'].idxmax(), :]
        r2 = best_estimator_results.mean_test_r2
        negRMSE = best_estimator_results.mean_test_neg_root_mean_squared_error
        negMAE = best_estimator_results.mean_test_neg_mean_absolute_error
        timeDur = modelObjects[modelName+'Time']     
        estimationCompare.update({modelName: [r2, negRMSE, negMAE, timeDur]})
        
        theBestEstimators[modelName] = modelObjects[modelName].best_estimator_
        theBestParameters[modelName] = modelObjects[modelName].best_params_

    estimationCompare = pd.DataFrame(estimationCompare)
    estimationCompare.index = ["R_squared", "negtiveRMSE", "negativeMAE", "model_time"]

    return theBestEstimators, theBestParameters, estimationCompare
In [50]:
# Call the function on our models
[theBestEstimators, theBestParameters, estimationCompare] = estimationResult(modelObjects)
print('The best parameters: >> \n')
display(theBestParameters)
print("")
print('The best parameters performance: >> \n')
display(estimationCompare)

The best parameters: >> 


{'elasticNet': {'alpha': 0, 'l1_ratio': 0},
 'KNN': {'n_neighbors': 7, 'weights': 'distance'},
 'treeReg': {'max_depth': 10, 'min_samples_leaf': 5},
 'rForest': {'max_features': 4, 'min_samples_split': 2, 'n_estimators': 160},
 'NN': {'activation': 'relu',
  'hidden_layer_sizes': (50, 25),
  'max_iter': 500,
  'solver': 'lbfgs'},
 'XGBoost': {'learning_rate': 0.1, 'min_child_weight': 2, 'n_estimators': 500}}
The best parameters performance: >>
elasticNet KNN treeReg rForest NN XGBoost
R_squared 0.432450 0.548519 0.529886 0.631726 0.568520 0.617485
negtiveRMSE -0.549280 -0.489909 -0.499901 -0.442473 -0.478939 -0.450943
negativeMAE -0.423531 -0.370049 -0.381326 -0.331704 -0.366401 -0.341874
model_time 6.907512 5.705644 2.125764 246.322631 189.357964 25.794870

Model selection and final results ¶

In [51]:
# Predict on test data
resultTable = {}
predValue = {}

for modelName , _ in modelsHyper:
    y_pred = theBestEstimators[modelName].predict(X_test)
    r2 = metrics.r2_score(y_test, y_pred)
    rmse = metrics.root_mean_squared_error(y_test, y_pred)
    mae = metrics.mean_absolute_error(y_test, y_pred)
    
    resultTable.update({modelName: [r2, rmse, mae]})
    predValue.update({modelName: np.exp(y_pred)})

resultTable = pd.DataFrame(resultTable)
resultTable.index = ["R_squared", "RMSE", "MAE"]
predValue = pd.DataFrame(predValue)
predValue["actual"] = np.exp(y_test.reset_index(drop=True))

print("models performance >>")
display(resultTable.head())
print("")
print("predictions overview >>")
display(predValue.head())

models performance >>
elasticNet KNN treeReg rForest NN XGBoost
R_squared 0.428820 0.550777 0.527026 0.628726 0.559714 0.612262
RMSE 0.548291 0.486245 0.498934 0.442050 0.481384 0.451745
MAE 0.420852 0.364293 0.378543 0.328440 0.366579 0.340195 
predictions overview >>
elasticNet KNN treeReg rForest NN XGBoost actual
0 176.264028 313.077243 222.535772 201.265830 192.295302 233.499146 190.0
1 181.782357 117.195900 113.188846 140.684069 136.470340 112.258232 88.0
2 188.819486 920.540303 1095.451614 897.484376 770.094697 901.483215 818.0
3 193.325770 175.954067 195.419574 200.370328 139.246285 203.780167 186.0
4 190.426720 222.341856 145.279208 210.457666 236.723871 187.182465 280.0
In [52]:
# Feature importance of the best model
impt = theBestEstimators["rForest"].feature_importances_
plt.barh(X_test.columns,impt)
plt.title('Feature importance')
plt.show()
No description has been provided for this image
In [53]:
# Predicted values from the best model vs actual values
# Randomly select 30 points to view the differences between predicted and actual values
[fig, axes] = plt.subplots(3, 3, figsize=(10,10))
for ax in axes.flat:
    randVal = np.random.choice(predValue.index, 30)
    x = np.arange(1, 31)
    yF = predValue["rForest"][randVal]
    yA = predValue["actual"][randVal]
    ax.scatter(x, yF)
    ax.scatter(x, yA)
    ax.plot((x,x),(yF, yA),"k:")
    ax.set_ylim(0,1500)
    plt.sca(ax)                                  
    plt.yticks(np.arange(0,1501,100),fontsize=8)
    ax.legend(["rForest", "actual"])
    ax.grid()
fig.tight_layout()
No description has been provided for this image

Main Findings:

  • The best model for price prediction is the Random Forest.
  • The model explains about 63% of the variation in price.